I just bought a new ESP8266 developpment board. When I reset it I must set the baudrate at 74880. The board did't seem to accept AT command from a CoolTerm terminal.
After a reset, these info are sent to the serial monitor
Hi @arjfca. Please tell us the reason you want to send AT commands to the ESP8266.
The AT firmware is useful if you want to use the ESP8266 as a Wi-Fi adapter for another Arduino board. However, most people these days just program the ESP8266 directly with an Arduino sketch, without bothering with the complexity of having two microcontrollers in the project. If you don't need to connect another Arduino board to the ESP8266, then there is no need for the AT firmware and you can skip that somewhat complicated process of installing it.
For the reboot output that is the correct baud-rate, but most likely the Firmware that is loaded uses 115200kbps.
Try that and make sure you send 'Both CR & LF' as a line ending.